I think that geometry is a form of accelerated calculation and presentation
of distances and angles by/in the mind, of the external mathematical
reality.

Within this mental geometrical representation,  we locate the rest of the
elements of the mathematical reality that are relevant for survival, they
are, the qualia. And this is what whe perceive as "reality", that apears to
be "out there".

I mean 3D geometry. any other geometry either is mentaly transated to 3D by
projections or else, must be calculated non intuitively (non accelerated)
 by means of algebraic formulas.

However, I imagine that an advanced robot with fast spatial processing
(based of algebraic formulas) would pass the turing test when asked about
geometrical figures in space. It can even answer: "geometry is intuitive
form me. My father-engineer gave me a good floating point coprocessor and
good spatial algorithms.

but there is a self reference when we try to imagine how the brain or a
computer process geometry, and we imagine them embedded in the space and
time that they create, which is not a correct intuition. we must imagine it
in no time and no space. IMHO.


2013/2/4 Craig Weinberg <whatsons...@gmail.com>

>
>
> On Monday, February 4, 2013 12:01:38 PM UTC-5, Bruno Marchal wrote:
>>
>>
>> On 01 Feb 2013, at 22:09, Craig Weinberg wrote:
>>
>> I have mentioned this before, but it keeps haunting me.
>>
>> If geometry did not exist.
>>
>> Could you invent it with mathematics alone?
>>
>> And if you could do that...
>>
>> Why would you?
>>
>> For instance: A triangle can be defined mathematically in different ways,
>> but without the inherently geometric presentations of lines and angles, it
>> seems that all you could generate is a description of a set of values which
>> have the same relation as the values which would be present if a geometric
>> shape were measured or sampled from optical or tactile detections.
>>
>> That is not to say that the list of mathematical definitions which
>> satisfy triangularity (a^2 + b^2 = c^2 for example), even an exhaustive
>> list, would suggest anything like the visible presence of a shape. All of
>> the mathematics can be done completely in the dark, and no realism of
>> points, plots, displays, manifolds, topologies, etc, ever need to literally
>> appear to anything.
>>
>>
>> We don't know that.
>>
>
> We don't know that we don't know that.
>
> Craig
>
>>
>> Bruno
>>
>>
>>
>> So why do they?
>>
>> Craig
>>
>>
>>
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-- 
Alberto.

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